Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3799 | C2 | semidirect |
| 2. C2×#3745 | C2 | semidirect |
| 3. #63909 | C2 | semidirect |
| 4. C2×#3717 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. #63564 | C2 | semidirect |
| 37. (C2×D3)⋊C8 | D3 | semidirect |
| 38. #816 | D3 | semidirect |
| 47. C4⋊(C3⋊D3) | D4 | semidirect |
| 54. C3×Dic6 | D4 | semidirect |
| 159. Dic6 | D12 | semidirect |
| 225. C32 | #449 | semidirect |
| 279. C3 | #4734 | semidirect |
| 280. C3 | #4810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3799 | 2 |
| C2×#3745 | 2 |
| #63909 | 2 |
| C2×#3717 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#816 | 2 |
| #63564 | 2 |
| #4810 | 3 |
| #4734 | 3 |